Matt Garza has left the Chicago Cubs for the Texas Rangers, in a trade that will send at least four men the other way. Photograph: John Sommers II/Reuters

The Texas Rangers acquired Matt Garza from the Chicago Cubs in a trade that was completed on Monday, getting a pitcher they had long coveted just more than a week before the 31 July non-waiver trading deadline.

"He's an extremely talented pitcher that's had success in the toughest of divisions and the biggest of stages, who's throwing the ball as well as anybody right now," Rangers general manager Jon Daniels said. "It's a power repertoire, a little bit of a different look from what we've got, and he was available. He was in our opinion the best guy on the market."

The 29-year-old right-hander provides a boost to a starting rotation plagued by injuries and a team that slipped three games behind Oakland in the AL West after being swept in a three-game weekend series at home against Baltimore.

Texas sent the Cubs the rookie right-hander Justin Grimm, top prospect third baseman Mike Olt and Class-A pitcher CJ Edwards. There will also be at least one player to be named later, possibly two, depending on who is chosen by Chicago.

"We paid a steep price in talent to acquire Matt, but we did so knowing that we've got other guys in the system," Daniels said. "What it comes down to, ultimately why we got him, beside the desire, is we had the players to do it."

Garza (6-1, 3.17 ERA), who can become a free agent after this season, has made 11 starts since missing the first seven weeks this season with a strained left shoulder muscle. He is 5-0 with a 1.24 ERA his last six starts. Garza had been scheduled to start Monday night for the Cubs in Arizona. He will instead start for the Rangers against the New York Yankees, likely Wednesday night.

Garza has a 63-62 career record in 181 major league games (178 starts) with Minnesota (2006-07), Tampa Bay (2008-10) and the Cubs (2011-13). He was a first-round draft pick by the Twins in the 2005 amateur draft.

"He was the best pitcher in baseball in his last five, six, seven starts. He's young, has great velocity, has good command of his pitches and that makes him attractive to any team," said the Cubs' manager, Dale Sveum. "It's not easy to part with a guy like Garza and someone has to step in and be productive. We hope the players we get will make us a better team, and in the future, we can be the team who purses a player like Garza."

The All-Star right-hander Yu Darvish came off the disabled list to start Monday night's game for the Rangers, at home against the New York Yankees in the opener of a four-game series. Darvish in essence missed only one start because of a right trapezius strain, but hadn't pitched since 6 July. The Yankees are now seven games off the pace in the AL East, after Darvish pitched six 1-3 scoreless innings, combining with three relievers on a shutout as the Rangers won 3-0. Darvish (9-4) threw 60 of 90 pitches for strikes.

Elsewhere, the Tampa Bay Rays beat the Boston Red Sox 3-0 to close within half a game of the Red Sox for the AL East lead, with Matt Moore pitching his first career shutout. The red-hot Rays won their 18th game from 20, coming from seven games off the lead and fourth place to now be in position to take over the divisional lead with a win on Tuesday. The Baltimore Orioles stayed only a game behind the Rays by beating the Kansas City Royals 9-2 for a fifth-straight win.

Also on Monday, Andrew McCutchen hit a pair of two-run homers to lead the Pittsburgh Pirates over the struggling Washington Nationals, 6-5, and Bronson Arroyo pitched a shutout as the Cincinnati Reds routed the San Francisco Giants 11-0. The Atlanta Braves edged the New York Mets 2-1 in a game of crucial ninth-inning moments, and the Seattle Mariners extended their winning streak to seven by defeating the Cleveland Indians 2-1.

AJ Ellis hit a two-run homer and drove in a career-best five runs as the Los Angeles Dodgers cruised past the Toronto Blue Jays 14-5 to record a fourth-straight win. The rookie Junior Lake hit his first major league homer and drove in three runs to power the Cubs to a 4-2 win over the Arizona Diamondbacks. Max Scherzer outpitched Chris Sale in a matchup of All-Star starters as the Detroit Tigers beat the Chicago White Sox 7-3 but lost star slugger Miguel Cabrera to a hip injury.

Josh Reddick hit a two-run homer in the eighth inning to lift the Oakland A's to a 4-3 win over the Houston Astros. Clete Thomas homered and hit an RBI double, then took a catch at the fence to stop a go-ahead homer in the eighth inning, helping the Minnesota Twins to a 4-3 win over the Los Angeles Angels. Jesus Guzman homered and had three RBIs to lift the San Diego Padres over the Milwaukee Brewers 5-3, hours after the Brewers learned that Ryan Braun would be suspended for the rest of the season over a doping infringement.

Tom Koehler tossed seven strong innings while the Miami Marlins scored for the first time in four games, beating the Colorado Rockies 3-1.